Our moral responsibility for our actions seems to depend on our possession of a power to determine for ourselves what actions we perform - a power of self-determination. What kind of power is this? The paper discusses what power in general might involve, what differing kinds of power there might be, and the nature of self-determination in particular. A central question is whether this power on which our moral responsibility depends is by its nature a two-way power, involving a power over alternatives or a freedom to do otherwise. Criticism is made of various attempts to understand self-determination in one-way terms, whether as a capacity for rationality (McDowell) or as a form of voluntariness (Frankfurt). It is argued in particular that Frankfurt's arguments to show that moral responsibility does not depend on a freedom to do otherwise beg the question against his opponents